A chemist has a solution of 50% pure acid and another solution of 80% pure acid. How many gallons of each will make 600 gallons of 72% pure acid solution?

Question

 ?  gallons of 80% acid and
 ?    gallons of 50% acid.

Answer 1

Hi Franklin

 

Let x= the number of gallons of the 50% pure acid

     y= the number of gallons of 80% pure acid

 

x+y = 600....the number of gallons of the two different types of pure acids.....1

0.5x+0.8y = 0.72(x+y)......the acidic content of the mixture

0.5x+0.8y = 0.72(600)

0.5x+0.8y = 432 ...................................................2

So, we have two equations and two variables

 

x+y = 600

0.5x+0.8y = 432

 

multiply the first equation by 0.8

 

0.8x+0.8y = 480

0.5x+0.8y = 432

 

Subtract the second equation from the first

 

0.3x = 48

x = 160 gallons

 y = 600-160 = 440 gallons

 

Therefore, we need 160 gallons of 50% pure acid and 440 gallons of 80% pure acid.

 

I hope it helps.

A